Category: Curvature

True Horizon and Linear Perspective

In graphical, linear perspective, the horizon is the horizontal line where the vanishing points for level objects lie. However, as the Earth is a sphere, the horizon of linear perspective is not the same as the true horizon, which is the line that we observe separating Earth from the sky.

Flat-Earthers claim that the observed horizon is produced by the law of perspective. In reality, from a high vantage point, we can try extending level and parallel lines to find their vanishing points. In many cases, they will end up above the true horizon.

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Salar de Uyuni and Other Salt Flats

Salt flats are flat expanses of ground covered with salt and other minerals. Salar de Uyuni in Bolivia is the world’s largest salt flat. Salt flats appear visibly flat, but they still follow the curvature of Earth.

Flat-Earthers claim the apparent flatness of Salar de Uyuni and other salt flats “proves” a flat Earth. In reality, while salt flats appear flat, they still follow Earth’s curvature. On a salt flat, the bottom part of a distant object will be obscured by Earth’s curvature, similar to at sea.

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Airplanes Going Over Earth’s Curvature

To an observer on the ground, an airplane at 36000 ft will start going over Earth’s curvature at a distance of 400 km. However, we are also limited by atmospheric visibility. In an extremely best-case scenario, we can only see up to 240 km.

We can easily see ships going over Earth’s curvature, and flat-Earthers like to demand us the same thing for airplanes. In reality, at the typical distance a plane does that, it is far out of visibility range. But if it is very low, like when approaching a runway to land, it is possible to see the plane going over the curvature of the Earth.

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Archimedes and the Surface of any Fluid

In the 3rd century BCE, Archimedes of Syracuse wrote what we now call the Archimedes’ principle in his book “On Floating Bodies” using the spherical Earth model.

Flat-Earthers like to misuse Archimedes’ principle as if it supports their claim that Earth is flat. In particular, they abuse Archimedes’ principle as if it is a competing explanation against gravity. In reality, Archimedes and other Greek scientists at the time already knew Earth is a sphere, and he explicitly mentioned it in his writings.

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Observing Earth’s Curvature From a Flight

At the cruising altitude of a jet airliner, Earth’s curvature is too slight for us to notice casually. But with planning and careful observation, it is not impossible to see the curvature. Continue reading “Observing Earth’s Curvature From a Flight”

Curvature of Water Surface

If Earth is a sphere, why is the surface of water always flat?

Due to Earth’s gravity, water seeks the lowest potential or as close as possible to the center of Earth. It forms a practically spherical surface centered on Earth’s center. The width of the surface in everyday cases is tiny compared to Earth’s radius. Thus, the water surface looks practically flat but not perfectly flat.

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Where’s the Curvature?

A human eye can only visually perceive the curvature of the Earth if we are at a considerable altitude from the surface, which is still beyond the reach of most humans today. A commercial jet airliner is the highest position realistically attainable by most humans today. We can only perceive very slight curvature at such altitude and, even then, only in an ideal condition.

The basis of flat-Earthers’ belief is that the horizon appears flat. They would say if we cannot see the curvature, then there’s no curvature, and therefore, the Earth is flat. In reality, only a few people can travel high enough to see the curve.  The highest we can realistically go is by getting on a commercial jet airliner, which can only go about 11-15 km up, only a fraction of Earth’s radius.

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Curvature Dilemma

A ship disappearing from the bottom first is an effect of Earth’s curvature. It is not a direct observation of the curve itself. We can only directly see the curve from a high altitude, not from near the surface.

Flat-Earthers present this reality as if it is a dilemma: 1. Earth is too big for us to see the curvature, but 2. We can see ships go over the curvature. It is a false dilemma. Ships disappearing from the bottom first is an effect of Earth’s curvature. Such an observation is different from directly witnessing the curve itself.

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Artificial Horizon and Earth’s Curvature

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An artificial horizon, or attitude indicator, is a flight instrument that indicates the aircraft’s orientation relative to Earth’s horizon and gives an immediate indication of the smallest change of orientation. An artificial horizon utilizes a gyroscope to detect the change of orientation and pendulous vanes to continuously correct the orientation relative to the level.

Flat-Earthers claim that an artificial horizon should drift over time if the airplane is flying over the spherical Earth because the gyroscope will eventually drift and no longer points toward Earth’s center. In reality, an artificial horizon has a self-correcting mechanism, keeping the gyroscope upright if it is displaced for any reason, including by the aircraft’s motion following Earth’s curvature.

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Curved Airplane Window and Observation of Earth’s Curvature

With careful planning, we can easily observe Earth’s curvature from an airliner. To “explain” the observation, flat-Earthers invented the excuse that it is caused by the distortion from the shape of the airplane’s window.

In reality, all camera lenses are curved, too, yet most of these lenses produce normal, rectilinear images. The fact that the shape of the window is curved does not mean looking through the window will produce a curved horizon.

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Submarine’s Periscope

A periscope is an optical instrument that allows submarine operators to visually observe the situation above the surface while submerged. Like other optical devices, Earth’s curvature can obscure the visibility of a distant object.

Flat-Earthers claim a periscope can see objects that are too far, and they use it to “prove” a flat Earth. In reality, everything is consistent with spherical Earth. A ship 50 m (165 ft) high at a distance of 25 km (15.5 miles) can still be visible if the weather allows & the periscope is 2 m (7 ft) above the surface.

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Visibility of Africa from Spain and Vice Versa

The Strait of Gibraltar separates the Iberian Peninsula and Africa. The two are separated only by 13 km (8.7 miles) at the narrowest point. We can easily see Africa from Spain as it is not that far away and that there are many highlands on both sides.

Flat-Earthers present the visibility of Africa from Spain as “evidence” Earth is flat. In reality, Africa is not that far from Spain. It is not far enough for the curvature of Earth to obstruct our view of Africa from Spain and vice versa.

Curvature App

Curvature App is a web application we can use to create a simulation of the horizon’s shape and the visibility of distant objects on a flat and spherical Earth. Curvature App is available at walter.bislins.ch/Curve.

When determining a distant object’s visibility, flat-Earthers often use wrong calculators that fail to account for all the important variables and give them incorrect results. Curvature App accounts for all of these variables, and not only it gives us the numbers, but also the simulated view.

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Beyond Horizons: World Records of Farthest Pictures Taken on Earth

We can see an object farther over Earth’s curvature if we and the object are higher. Mountain peaks are the highest points on Earth. As a result, from a mountain peak, it is possible to observe another peak very far away, even over hundreds of kilometers. The website Beyond Horizons discusses these records of observation.

Flat-Earthers use some of the world records of the farthest peak to peak observation as “proof” of flat Earth. In reality, these observations are possible because the peaks are very high, and atmospheric refraction helps the observation. These observations agree with the expectation if Earth is a sphere.

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Statue of Liberty

The Statue of Liberty was once used as a lighthouse. Its light can be seen from 24 miles away. Like other lighthouses, it can produce the loom of the light due to scattering in the atmosphere, which allows its light to be seen from much farther away.

Flat-Earthers use the visibility of the Statue of Liberty from 60 miles away as “evidence” of flat Earth. In reality, the effect of the loom of the light is what might be visible under clear weather, but the structure itself is not. Today, the Statue of Liberty is no longer used as a lighthouse, and nothing of it can be seen from that far away. But the information still spreads in flat-Earth communities as a hoax.

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Bonneville Salt Flat and Earth’s Curvature

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Interstate 80 traverses the Bonneville Salt Flat, Utah, in a practically straight segment. From the hilly terrain to the west of the highway, we can observe the highway’s curve following Earth’s curvature using a long-zoom camera.

Flat-Earthers incorrectly claim that salt flats are perfectly flat and use them to “prove” a flat Earth. In reality, salt flats form a curve following Earth’s curvature, like the ocean’s surface.

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Exalt’s Mediterranean Microwave Transmission Link

One of the longest microwave links is between Lebanon and Cyprus, spanning 235 km (146 miles). To clear Earth’s curvature, both transceivers need to be placed on high ground. In the illustration, we provide an example where we can install both transceivers to establish the link.

Flat-Earthers claim that the link can only be established if Earth is flat. In reality, it is trivial to find locations in Lebanon and Cyprus where we can set up a microwave link between them that clears Earth’s curvature without using any towers and still leaves us with plenty of wiggle room.

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Objects Obscured by Earth’s Curvature and Zoom Factor

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From an observer on a shore, the distance to the horizon is 5 km (3 miles), or more if the observer is higher. Therefore, Earth’s curvature obscures objects starting from that distance. If the objects are not large enough, we need an optical aid, like zooming in using a camera, to see them in the first place.

Flat-Earthers often show us wide-angle photos to demonstrate that objects are not obscured by Earth’s curvature. In reality, in such photos, objects far enough to be obscured by Earth’s curvature cannot be resolved. It is hard to see objects obscured by Earth’s curvature if the objects themselves are not visible in the picture.

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Magnetic Dip

A magnetic compass is less usable near the poles partly due to magnetic dip. One of the Earth’s poles is much closer and affects the needle more strongly than the other pole. As a result, Earth’s magnetic field pulls the needle toward the ground.

Flat-Earthers claim that a compass is unusable only near Antarctica. In reality, the same also occurs near the North Pole. Magnetic dip, as observed on various locations on Earth, can only happen if the Earth is spherical.

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“Stuff is Flat”: Incorrect Neil deGrasse Tyson’s Claim About the Observation of Earth’s Curvature

Neil deGrasse Tyson once incorrectly stated that it is still too close to the surface to see Earth’s curvature from the height of Felix Baumgartner’s jump. In reality, we should be able to see it using our eyes.

Flat-Earthers believe people take Neil’s remarks as gospel and use Neil’s incorrect statement to dismiss any observation of Earth’s curvature. However, we have no problem saying that Neil was wrong. It is OK to be wrong as long as we are willing to revise our views when faced with new facts, and we are certain Neil will.

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